why can't a large population exist without importing food?

Answer 1

A large population can exist without importing food. Technology has allowed agricultural harvests to increase significantly, allowing more to be produced than is needed. Look at the US, for instance. Farmers are paid by the government to destroy a portion of their crops in order to keep the price from falling below a certain level. Yet Americans generally have plenty to eat. If we really wanted to remain totally self-sufficient in our food supply, it could be achieved.

Answer 2

It is not the size of the population but the farmland available per consumer of food, and the land intensity of production of the farming techniques. Hence in a high-protein consuming society (ie, Japan, the U.S.) the average diet requires much more land due to the need for cattle to be fed large amounts of grain and corn. However, a more vegetarian society would allow a variety of crops to be grown on a smaller portion of land to feed the same person.

There's also a matter of incomes. In nations with high incomes, regardless of size of land available for agrarian production, there is more of a taste (and income available for) consumption of expensive imported foods such as fine cheeses, wines, etc.

So a large population can exist without imports but it generally has chosen not to do so.